I studied antibiotic resistance when I worked in pharma. It's a fiendishly difficult problem. You have a mix of factors that all conspire to a bad outcome. First, you have natural selection, so any antibiotic safe for human consumption is likely to eventually result in drug resistant bacteria. Secon, you have social practices. In the US you have patients who brow beat their doctors into giving them antibiotics when they don't need them. In other parts of the world, you can buy antibiotics over the counter! This is hugely problematic since the genes for resistance spread globally when they get a foothold (you can actually watch this over time with DNA sequencing and careful collection of samples). Finally, on the economic side, most regulators like the FDA will force any new antibiotic to be held back on the shelf and used only as a "drug of last resort". This reduces incentives to develop new antibiotics since the drug patent will expire before you can sell enough to make back the R&D cost. Much better to throw resources at cancer since your drug might end up as a front line therapy there, than to waste time on antibiotics (so the bean counter thinking goes).

I honestly don't know what the answer is. Most likely, there will need to be some new tech the bugs have a hard time beating. Outside the body we still have plenty of things that kill bacteria which they can't get around (bleach comes to mind). The likely outcome is some kind of new delivery mechanism that is fast, complete, and highly effective.